Heat exchangers for cooling recirculated exhaust gas are known from the prior art. In general, in the case of exhaust-gas cooling, there is the problem of the high chemical aggressiveness of the exhaust gas and the low pH value of its condensates. For this reason, only exhaust-gas heat exchangers produced from austenitic steels with high corrosion resistance have existed previously. Steels of said type result in high material costs and often further follow-up costs on account of the more complex machining operations. Furthermore, austenitic steels are usually poor heat conductors, such that heat exchangers with a predefined cooling power are of relatively large and heavy construction.